Question

A 22 kg solid door is 220 cm tall, 91 cm wide. a) What is the door's moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge? b) What is the door's moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge?

Answer 1

Answer

given,

mass of the solid door = 22 Kg

dimension of door = 220 cm x 91 cm

moment of inertia about the hinge

   $I = \dfrac{1}{3}Mr^2$

r is the distance from the one edge which is equal to 91 cm or 0.91 m

   $I = \dfrac{1}{3}\times 22 \times 0.91^2$

   $I = 6.073\ kg m^2$

Moment of inertia about center for rectangular gate is equal to

   $I_{CM} = \dfrac{1}{12}Mr^2$

moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge

   $I = I_{CM} + MR^2$

   $I = I_{CM} + M(\dfrac{91}{2}- 15)^2$

   $I = \dfrac{1}{12}Mr^2+ M(0.0930)$

  $I = \dfrac{1}{12}\times 22 \times 0.91^2+ 22 \times (0.093)$

  $I = 3.56\ Kg m^2$